Is there an easy way/algorithm to match 2 clouds of 2D points?

Question

I am wondering if there is an easy way to match (register) 2 clouds of 2d points.

Let\'s say I have an object represented by points and an cluttered 2nd image with t

Answer 1

The KLT (Kanade Lucas Tomasi) Feature Tracker makes a Affine Consistency Check of tracked features. The Affine Consistency Check takes into account translation, rotation and scaling. I don't know if it is of help to you, because you can't use the function (which calculates the affine transformation of a rectangular region) directly. But maybe you can learn from the documentation and source-code, how the affine transformation can be calculated and adapt it to your problem (clouds of points instead of a rectangular region).

Answer 2

I believe you are looking for something like David Lowe's SIFT (Scale Invariant Feature Transform). Other option is SURF (SIFT is patent protected). The OpenCV computer library presents a SURF implementation

Answer 3

Let me first make sure I'm interpreting your question correctly. You have two sets of 2D points, one of which contains all "good" points corresponding to some object of interest, and one of which contains those points under an affine transformation with noisy points added. Right?

If that's correct, then there is a fairly reliable and efficient way to both reject noisy points and determine the transformation between your points of interest. The algorithm that is usually used to reject noisy points ("outliers") is known as RANSAC, and the algorithm used to determine the transformation can take several forms, but the most current state of the art is known as the five-point algorithm and can be found here -- a MATLAB implementation can be found here.

Unfortunately I don't know of a mature implementation of both of those combined; you'll probably have to do some work of your own to implement RANSAC and integrate it with the five point algorithm.

Edit:

Actually, OpenCV has an implementation that is overkill for your task (meaning it will work but will take more time than necessary) but is ready to work out of the box. The function of interest is called cv::findFundamentalMat.

Answer 4

I would try and use distance geometry (http://en.wikipedia.org/wiki/Distance_geometry) for this

Generate a scalar for each point by summing its distances to all neighbors within a certain radius. Though not perfect, this will be good discriminator for each point.

Then put all the scalars in a map that allows a point (p) to be retrieve by its scalar (s) plus/minus some delta
M(s+delta) = p (e.g K-D Tree) (http://en.wikipedia.org/wiki/Kd-tree)

Put all the reference set of 2D points in the map

On the other (test) set of 2D points:
foreach test scaling (esp if you have a good idea what typical scaling values are)
...scale each point by S
...recompute the scalars of the test set of points
......for each point P in test set (or perhaps a sample for faster method)
.........lookup point in reference scalar map within some delta
.........discard P if no mapping found
.........else foreach P' point found
............examine neighbors of P and see if they have corresponding scalars in the reference map within some delta (i.e reference point has neighbors with approx same value)
......... if all points tested have a mapping in the reference set, you have found a mapping of test point P onto reference point P' -> record mapping of test point to reference point ......discard scaling if no mappings recorded

Note this is trivially parallelized in several different places

This is off the top of my head, drawing from research I did years ago. It lacks fine details but the general idea is clear: find points in the noisy (test) graph whose distances to their closest neighbors are roughly the same as the reference set. Noisy graphs will have to measure the distances with a larger allowed error that less noisy graphs.

The algorithm works perfectly for graphs with no noise.

Edit: there is a refinement for the algorithm that doesn't require looking at different scalings. When computing the scalar for each point, use a relative distance measure instead. This will be invariant of transform

Answer 5

From C++, you could use ITK to do the image registration. It includes many registration functions that will work in the presence of noise.

Answer 6

You want want the Denton-Beveridge point matching algorithm. Source code at the bottom of the page linked below, and there is also a paper that explain the algorithm and why Ransac is a bad choice for this problem.

http://jasondenton.me/pntmatch.html